Abstract：The fractal property is considered as the third fundamental topology features of complex networks. Studies on the fractal property of complex networks are of great significance for understanding the structure complexity of the network. The information dimension method is a useful tool to measure the fractal property of complex networks. The existing information dimension method is mainly used to analyze the fractal property of unweighted networks, and it is not fully applicable to analyze the fractal property of weighted networks. In this paper, motivated by the idea of box-covering algorithm for weighted complex networks, a fractal analysis method of weighted networks based on information dimension is proposed. We first apply this method to study the fractal property of a family of constructed “Sierpinski” weighted fractal networks, the results show that the fractal dimension of these networks obtained by the proposed method are very close to its theoretical similarity dimension. Then, we apply the proposed method to study the fractal property of three real-world weighted networks and make a detail comparison with the box-covering algorithm, results demonstrate that the proposed method is effective for the fractal scaling analysis of real-world weighted complex networks.
黄毅, 张胜, 戴维凯, 王硕, 杨芳. 基于信息维数的加权网络分形特性分析[J]. 复杂系统与复杂性科学, 2018, 15(2): 26-33.
HUANG Yi, ZHANG Sheng, DAI Weikai, WANG Shuo, YANG Fang. Fractal Analysis of Weighted Networks by a Modified Information Dimension Method. Complex Systems and Complexity Science, 2018, 15(2): 26-33.
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